Cold turkey quickest. Took dd1 about 4 months in pull-ups + pants mixed. Dd2 was dry in 2 days cold turkey, ds has been a bit more variable, but is dry most days (think is day 11 now). Trying him at night too now (fingers crossed). For 5 nights his nappy was dry in the morning, but last night he had wet nappy, in fact wet even before bed. He was then wet in the morning when I changed him into pants. I know he can go through night, but when he sometimes has nappy he gets confused/lazy when it comes off. Have waterproof under sheet and another set of sheet/waterproof in case he is wet and a new tumble dryer, so all set!
You can start slowly by just having some nappy free time each day, esp good outside in the warmer weather, so you and they get used to it, and you might catch some which obviously you praise as if was the best thing ever.
I haven't bothered with pull ups for second two, as they are more expensive and harder for them to distinguish between pull-ups and pants, so makes them more confused about when they can and can't wee in them. I can see that they might have a place e.g. At school/nursery so child can go themselves with less assistance, but I don't think that they help with potty training, and sooner or later you have to make the transition anyway.
Oh last tip, make sure that not only do you have lots of pants (10 is ideal); but also loads of trousers/ socks if you start now and it's a boy, we are short on socks, so having superfast turnaround on them! Girls with just dresses on make bigger puddles, as with a boy by the time it gets to floor level it has soaked into pants, trousers and socks, not too much left!